Young man, in mathematics you don't understand things. You just get used to them.
- John von Neumann

Below are various notes collected from my time in graduate school, in the off chance that they might be useful to others.

2021-08-03 / My Ph.D. thesis in mathematical physics, written under the guidance of Ezra Getzler, concerns a new construction of the Batalin-Vilkovisky (BV) Laplacian using the methods of homological perturbation theory. [thesis] [slides]

2019-05-XX / In a classic paper, Bott computes the differential forms on the classifying space of a compact Lie group G. In this talk I outline this construction and briefly describe how to view this computation as a concrete construction of a shifted symplectic structure (a la Pantev-Toen-Vaquie-Vezzosi) on the classifying stack BG represented by a simplicial smooth manifold. I recommend Ezra Getzler's exposition on simplicial manifolds as a general reference. [talk notes]

2018-XX-XX / Rough notes on derived geometry taken during lectures given by various speakers at the Fields Institute in a summer conference. [lecture notes]

2018-01-XX / Very unfinished notes on differential cohomology and gerbes, in which I took a concrete and computational approach. Reader assumes responsibility for any and all injuries incurred. [unfinished notes]

2018-XX-XX / Rough notes on Mihnea Popa's course on complex geometry. [notes]

2017-09-17 / Lightning talk on the Atiyah-Singer index theorem. [notes]

2017-XX-XX / Rough notes from John Francis' course on factorization homology. [notes] [high-level summary]

2017-04-10 / In this talk (for John Francis' Milnor seminar) I introduce the basics of Chern-Weil theory. [talk notes]

2017-03-17 / An informal reading group on WKB methods (led by Aaron Naber) led to this high-level talk on Witten's de Rham approach to Morse theory, and Fukaya's reinterpretation in terms of A-infinity categories. [talk notes]

2017-01-10 / I gave a talk on the symplectic geometry behind classical mechanics (with an eye towards moment maps and Noether's theorem) for a seminar on the BV formalism, run by Sean Pohorence. [talk notes]

2016-11-30 / I gave a talk (for John Francis' Kan seminar) sketching Bousfield's construction of the localization of spaces with respect to homology equivalences. I seem to have avoided discussing all the hard parts of the construction... clearly I'm not the sharpest tool in the shed. [talk notes]

2016-01-13 / For a seminar on Reshetikin-Turaev invariants, led by Theo Johnson-Freyd, I gave a talk on the geometric quantization of Chern-Simons theory (according to Axelrod, della Pietra, and Witten). [talk notes]

2015-12-11 / I spent a bit of time learning about the basics of symplectic geometry as a first-year graduate student under Eric Zaslow's patient eye. [notes]

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